https://file.aiquickdraw.com/mathbot/file/1727912273788ixkhphqi.jpg

The graph shown in the image is of a **V-shaped function**, likely representing an **absolute value function**. The vertex of the graph is at the point \((0, -2)\), and the arms of the graph open upwards. 

### Domain and Range Analysis:
- **Domain**: The domain represents all possible \(x\)-values that the function can take. From the graph, we see that the function extends infinitely in both directions horizontally, which means **the domain is all real numbers**: 
  \[
  \text{Domain} = (-\infty, \infty) \quad \text{or} \quad \text{all real numbers}.
  \]

- **Range**: The range represents all possible \(y\)-values that the function outputs. The lowest point on the graph is \(y = -2\), and the graph increases from there as \(x\) moves in either direction. Therefore, the **range is \(y \geq -2\)**:
  \[
  \text{Range} = [-2, \infty).
  \]

Thus, the answers provided in the image, stating the domain as **all real numbers** and the range as **\(y \geq -2\)**, are correct.

Would you like further details or explanations? 

Here are 5 follow-up questions based on this explanation:
1. How do you find the domain of different types of functions?
2. Can an absolute value function have a different vertex than \((0, -2)\)?
3. What are the general properties of an absolute value function?
4. How do you determine the range of a function graphically?
5. How does the slope of the arms in an absolute value function affect the graph?

**Tip**: Always check the vertex of an absolute value function to determine its minimum or maximum, which helps in defining the range.

Find the domain and range of the function shown in the graph.

Learn how to find the domain and range of an absolute value function based on its graph. This example explores an absolute value function with the vertex at (0, -2), covering important concepts for students in Grades 7-10.

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